Scabies in residential care homes: Modelling, inference and interventions for well-connected population sub-units

In the context of an ageing population, understanding the transmission of infectious diseases such as scabies through well-connected sub-units of the population, such as residential care homes, is particularly important for the design of efficient interventions to mitigate against the effects of those diseases. Here, we present a modelling methodology based on the efficient solution of a large-scale system of linear differential equations that allows statistical calibration of individual-based random models to real data on scabies in residential care homes. In particular, we review and benchmark different numerical methods for the integration of the differential equation system, and then select the most appropriate of these methods to perform inference using Markov chain Monte Carlo. We test the goodness-of-fit of this model using posterior predictive intervals and propagate forward the resulting parameter uncertainty in a Bayesian framework to consider the economic cost of delayed interventions against scabies, quantifying the benefits of prompt action in the event of detection. We also revisit the previous methodology used to assess the safety of treatments in small population sub-units—in this context ivermectin—and demonstrate that even a very slight relaxation of the implicit assumption of homogeneous death rates significantly increases the plausibility of the hypothesis that ivermectin does not cause excess mortality based upon the data of Barkwell and Shields.Author summary: Our work makes five main contributions. (1) We study a previously under-modelled scenario—transmission of scabies in residential care homes—that is of significant and growing public health importance in the context of an ageing population. (2) We develop a Markov-chain-based modelling framework that accurately captures the disease dynamics in well-connected sub-units such as care homes, but whose use has previously been limited due to computational cost. (3) We demonstrate that appropriate numerical methods (in particular rational Krylov approaches) for the solution of the mechanistic model for transmission of scabies in care homes speeds up evaluation by several orders of magnitude compared to other methods. (4) We demonstrate a Bayesian approach in which the model is fitted to data using computationally-intensive MCMC methods, validated using posterior predictive intervals, and has its uncertainty quantified in forward predictions. (5) We revisit the question of safety of ivermectin using appropriate methods and demonstrate that relaxation of the assumption of homogeneous death rates can make previous influential conclusions on lack of safety unsound.